Blog Archives

Topic Archive: provability logic

Computational Logic SeminarTuesday, May 3, 20162:00 pmGraduate Center, rm. 4422

Lev Beklemishev

Some abstract versions of Goedel’s Second Incompleteness Theorem based on non-classical logics

Steklov Mathematical Institute of Russian Academy of Sciences in Moscow

We study abstract versions of Goedel’s second incompleteness theorem and formulate generalizations of Loeb’s derivability conditions that work for logics weaker than the classical one. We isolate the role of the contraction and weakening rules in Goedel’s theorem and give a (toy) example of a system based on modal logic without contraction invalidating Goedel’s argument. On the other hand, Goedel’s theorem is established for a version of Peano arithmetic without contraction. (Joint work with Daniyar Shamkanov)

Computational Logic SeminarTuesday, November 5, 20132:00 pmGraduate Center, rm. 3209

Elena Nogina

Reflection Principles Involving Provability and Explicit Proofs

The City University of New York

Reflection principles are classical objects in proof theory and the areas studying Gödel’s Incompleteness. Reflection principles based on provability predicates were introduced in the 1930s by Rosser and Turing, and later were explored by Feferman, Kreisel & Levi, Schmerl, Artemov, Beklemishev and others.

We study reflection principles of Peano Arithmetic involving both Proof and Provability predicates. We find a classification of these principles and establish their linear ordering with respect to their metamathematical strength.